Publication result detail

A ternary relation for structuring the digital plane

ŠLAPAL, J.

Original Title

A ternary relation for structuring the digital plane

English Title

A ternary relation for structuring the digital plane

Type

Paper in proceedings (conference paper)

Original Abstract

We discuss certain ternary relations, called plain, and show that each of them induces a connectedness on its underlying set. This connectedness allows for definitions of concepts of simple closed and Jordan curves. We introduce a particular plain ternary relation on the digital plane Z^2 and, as the main result, we prove a digital analogue of the Jordan curve theorem for the connectedness induced by this relation. It follows that the ternary relation introduced may be used as a convenient structure on the digital plane for the study of the geometric properties of digital images that are related to boundaries because boundaries of objects in digital images are represented by digital Jordan curves. An advantage of this structure over the Khalimsky topology is that it allows Jordan curves to turn at the acute angle /4 at some points.

 

English abstract

We discuss certain ternary relations, called plain, and show that each of them induces a connectedness on its underlying set. This connectedness allows for definitions of concepts of simple closed and Jordan curves. We introduce a particular plain ternary relation on the digital plane Z^2 and, as the main result, we prove a digital analogue of the Jordan curve theorem for the connectedness induced by this relation. It follows that the ternary relation introduced may be used as a convenient structure on the digital plane for the study of the geometric properties of digital images that are related to boundaries because boundaries of objects in digital images are represented by digital Jordan curves. An advantage of this structure over the Khalimsky topology is that it allows Jordan curves to turn at the acute angle /4 at some points.

 

Keywords

Ternary relation, connectedness, digital plane, Jordan curve theorem

Key words in English

Ternary relation, connectedness, digital plane, Jordan curve theorem

Authors

ŠLAPAL, J.

RIV year

2018

Released

28.02.2017

Publisher

EDP Sciences

Location

Les Ulis Cedex A

Book

AMCSE 2016

ISBN

2271-2097

Periodical

ITM Web of Conferences

Volume

9

Number

01012

State

French Republic

Pages from

1

Pages to

5

Pages count

5

URL

https://www.fit.vut.cz/research/publication/11594/

Full text in the Digital Library

http://hdl.handle.net/11012/195570

BibTex

@inproceedings{BUT144501,
  author="Josef {Šlapal}",
  title="A ternary relation for structuring the digital plane",
  booktitle="AMCSE 2016",
  year="2017",
  journal="ITM Web of Conferences",
  volume="9",
  number="01012",
  pages="1--5",
  publisher="EDP Sciences",
  address="Les Ulis Cedex A",
  doi="10.1051/itmconf/20170901012",
  issn="2271-2097",
  url="https://www.fit.vut.cz/research/publication/11594/"
}

Documents

itmconf_amcse2017_01012
ITMWebocConf2017_01012